Researches concerning the use of rare-earth ions in a crystal as a laser medium have been made for a long time. However, in view of the fact that the coherence times of the optical transition and hyperfine transition of these ions are longer than the other solid materials, applications of the ions to quantum information technology have recently been developed (see, for example, Y.-F. Xiao, Z.-F. Han, Y. Yang. and G.-C. Guo, Phys. Lett. A 330, 137 (2004)).
When certain optical transitions of a rare-earth ion in a crystal are utilized for devices (hereinafter referred to as “quantum information devices”), such as quantum computers, quantum memories, used in quantum information technology, it is very convenient if their transition wavelengths fall within the optical telecommunication wavelength range (1260 to 1.625 nm), for the following reasons 1 to 3:
1. The existing semiconductor lasers can be utilized.
2. When an optical resonator that has a resonator mode that resonates with one of the transitions is used to perform a quantum gate operation, the wavelength corresponding to the resonator mode is longer than that of visible light, whereby scattering loss in the resonator is less than the case of using the visible light.
3. Those devices are suitable for applications to telecommunication devices (such as quantum memories and distributed quantum computers used for quantum communications and quantum cryptography).
As a transition within the optical telecommunication wavelength range well examined so far, 4I15/2-4I13/2 transition (approx. 1550 nm) of Er3+ can be taken. This is, however, not a satisfactory transition if it is applied to quantum information devices, for the following reasons (i) to (iv):
(i) Since Er3+ is a so-called Kramers ion having an odd number of 4f electrons, it has a large electronic magnetic moment in its ground states, and therefore, a large magnetic field must be applied to obtain a long coherence time (for optical transition) (see, for example, Y. Sun et al., J. Lumin. 98, 281 (2002)).
(ii) When the electronic magnetic moments in the ground states are used as quantum bits, the coherence time is relatively short (compared to, for example, the case of using the nuclear spins of a Pr3+ ion of Pr3+:Y2SiO5).
(iii) From the viewpoint of coherence time, it is desirable to use nuclear spins (hyperfine levels) as quantum bits. It is known that the coherence time of each nuclear spin can be extended if an appropriate magnetic field is applied (see, for example, E. Fraval, M. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95, 030506 (2005)). However, this method cannot be employed in the case of Er3+ because of the above-mentioned large magnetic field that must be applied to reduce the influence of the electronic magnetic moment.
(iv) Since the transition dipole moment is small, if an optical resonator is utilized to, for example, perform a quantum gate operation, the coupling constant with the resonator mode will be small.
The first-mentioned three of the disadvantages of the Er3+ ion can be overcome if a non-Kramers ion having an even number of 4f electrons is used. The 3H4-3F3 transition of a Pr3+ ion is the most promising among non-Kramers ion transitions at an optical telecommunication wavelength. Although the Pr3+ ion has the 3H4-3F4 transition as another candidate, the 3H4-3F3 transition of the Pr3+ ion is more desirable in consideration of the influence of multi-phonon relaxation described later, and therefore only the 3H4-3F3 transition will now be considered. Further, the 3H4-3F3 transition of the Pr3+ ion has a relatively large transition dipole moment (see, for example, “W. F. Krupke, Phys. Rev. 145, 325 (1966).” However, the applications of the 3H4-3F3 transition of the Pr3+ ion to quantum information devices have not been proposed yet.